Nevertheless, the integration of IRS into existing wireless networks faces new challenges, one of which is the optimization of the IRS reflection coefficients for facilitating the coherent superposition of dispersed intended signals and/or interference cancellation. Specifically, the optimization of the IRS reflection coefficients is generally coupled with the transmit beamforming design, which is different from the conventional systems without IRS [1]}. In [2]}, Wu et al. considered the IRS-assisted multi-input single-output (MISO) and multi-user MISO systems by formulating the transmit power minimizing problem, subject to the individual signal-to-interference-plus-noise-ratio (SINR) requirements at each user. The formulated problem is then solved by semidefinite relaxation (SDR) and alternating optimization (AO) algorithms to obtain the high-quality approximate solution of the transmit beamforming vectors for multiple users and reflection coefficients at the IRS. Besides, [2]} demonstrated that the IRS behaves quadratic power law with the number of reflecting elements, which is promising for energy-efficient deployment [4]}. Soon afterwards, [5]} extended the research results of [2]} upon considering the practical IRS elements with discrete phase shifters. Moreover, [5]} showed that, for the IRS equipped with a large number of reflecting elements, the power loss at the receiver relative to that equipped continuous phase shifters is about \(-3.9\)  dB for 1-bit quantized phase shifter and only \(-0.9\)  dB for 2-bit quantized phase shifter. Furthermore, [8]} investigated the capacity of IRS-assisted point-to-point multi-input multi-output (MIMO) systems, where the IRS reflection coefficients and transmit precoding are optimized alternatively by assuming that the other is given. Following this, the IRS assisted multi-user and multi-cell MIMO systems are reported in [9]} and [10]}, respectively, where the rate maximizing problem is solved by AO algorithm and fractional programming technique. The energy-efficiency maximization for IRS assisted multi-user MISO system is investigated in [11]}, where the AO algorithm assisted by the gradient descent and majorization-minimization (MM) algorithms are invoked to solve the formulated problem. Recently, the optimization of reflection coefficients at IRS has been performed under the joint consideration with other existing techniques, e.g., millimeter-wave (mmWave) communications [12]}, terahertz (THz) communications [13]}, [14]}, visible light communication (VLC) [15]}, orthogonal frequency division multiplexing (OFDM) [16]}, deep learning (DL) [17]}, [18]}, unmanned aerial vehicle (UAV) [19]}, [20]}, index modulation (IM) [21]}, non-orthogonal multiple access (NOMA) [22]}, [23]}, physical layer security (PLS) [24]}, [25]}, cell-free network [26]}, mobile edge computing (MEC) [27]}, and simultaneous wireless information and power transfer (SWIPT) [28]}, [29]}.
